Question

Let f denote an odd function and g an odd function. Decide whether the function h(x)=g(x) f(x) is even or odd.

Answer 1

h(-x) = f(-x)g(-x)

f(-x) = -f(x)

g(-x) = -g(x) ---->

f(-x)g(-x) = f(x)g(x) = h(x)

So:

h(-x) = h(x)

Answer 2

g(x)*f(x) is an even function, since both f and g change signs when x is replaced by -x